Algebra Basics Quiz

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Questions and Answers

What is the value of $x$ in the equation $3x + 7 = 16$?

  • 4
  • 5 (correct)
  • 3
  • 2

If the area of a triangle is given by the formula $A = \frac{1}{2}bh$, what is the area when the base $b$ is 10 and the height $h$ is 5?

  • 25 (correct)
  • 100
  • 50
  • 30

What is the slope of the line represented by the equation $y = 4x + 2$?

  • 0
  • -4
  • 2
  • 4 (correct)

If the roots of the quadratic equation $x^2 - 5x + 6 = 0$ are $p$ and $q$, what is the value of $pq$?

<p>6 (C)</p> Signup and view all the answers

What is the derivative of the function $f(x) = x^3 - 3x^2 + 4$?

<p>$3x^2 - 6x$ (C)</p> Signup and view all the answers

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Study Notes

Solving Linear Equations

  • The equation $3x + 7 = 16$ can be solved for $x$ by isolating the variable.
  • Subtract 7 from both sides to obtain $3x = 9$.
  • Divide both sides by 3 to get $x = 3$.

Calculating Triangle Area

  • The formula for the area of a triangle is $A = \frac{1}{2}bh$, where $b$ is the base and $h$ is the height.
  • Substitute $b = 10$ and $h = 5$ into the formula: $A = \frac{1}{2}(10)(5)$.
  • Simplify to get $A = 25$.

Identifying Slope

  • The equation $y = 4x + 2$ is in slope-intercept form ($y = mx + c$), where $m$ represents the slope.
  • Therefore, the slope of the line is $m = 4$.

Understanding Quadratic Roots

  • The product of the roots of a quadratic equation in the form $ax^2 + bx + c = 0$ is given by $c/a$.
  • In the equation $x^2 - 5x + 6 = 0$, the product of the roots $p$ and $q$ is $(6)/(1) = 6$.

Finding Derivatives

  • The derivative of a function $f(x) = x^n$ is given by $f'(x) = nx^{n-1}$.
  • Applying this to the function $f(x) = x^3 - 3x^2 + 4$, we get the derivative $f'(x) = 3x^2 - 6x$.

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